Mycroft Holmes, gives a cigarette to Sherlock and says "Merry Christmas". Then in the following scene, Dr. Watson asks Mycroft if he gave the cigarette to Sherlock.

So, it seems to me that the cigarette has some significance. Although it might also seem like Sherlock was just suffering from the supposed loss of Irene Adler, and his brother just thought the nicotine patches weren't good enough to help him relax.

When you go to the "Science of Deduction" blog, he has a study on smoking that he later removes. Like taxis, smoking is an important "thing." I need to find out which characters were smokers. Sherlock used patches while smoking. He may have used them to not become addicted while studying the tar. If it's "impossible" to find a place in London to smoke, maybe times and places when characters smoked are somehow important? My $0.02.
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user7330Dec 27 '13 at 5:44

7 Answers
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When Sherlock says "This is low tar", Mycroft replies "Well, you barely knew her". This reenforces the idea that the cigarette is a way of coping with the loss - he didn't know her that well, so he doesn't need a strong cigarette.

I presumed that it was just Mycroft and John Watson's way of telling whether Sherlock was badly affected by the news of her death. I think in the original A.C.D. stories, Sherlock Holmes does seem to have a tendency to fall into what we would now call depression and even that he has tendencies towards manic-depression. In the original stories he is also a user of drugs including opiates (which were not illegal at the time) when depressed.

I thought that (modern) Sherlock does not routinely smoke, therefore if he accepts the cigarette then he is going to be bad. I don't think it was just a way of helping him relax.

But he gets his required amount of nicotine from the patches. Why cigarette, then?
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Lelouch LamperougeJan 4 '12 at 22:13

@EknathIyer - but this reinforces the idea that it is not about relaxing him / keeping his nicotine levels up - but it is a diagnostic of his state of mind in general. If he needs a cigarette despite nicotine patches, then he must be depressed (well according to Mycroft & Watson anyway).
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iandotkelly♦Jan 4 '12 at 22:15

Hmm, probably I should watch it sometimes. The reviewers seem to like Sherlock.
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MnementhJan 5 '12 at 11:54

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@LelouchLamperouge The nicotine patches seem to be healthier than a cigarette and provide almost the same sensation. When he accepts to smoke, he doesn't seem to care about his own health anymore. So, indeed, it was a sign of depression.
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DragosJan 15 '12 at 16:08

@LelouchLamperouge Add one more. It's just that i joined the movie exchange late.
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DreddMay 17 '12 at 20:19

I can't be certain this is the right answer, but some of episode 2 makes it look like Sherlock's serious addiction is cigarettes not something a little more risque. So cigarettes are the modern stand-in for his need for cocaine.

Letting him have one is an admission that he has had to deal with something serious (like the loss of Adler).

Mycroft and Watson mentioned a "danger night." I assume Mycroft gave him the stick to be nice when seeing his brother emotionally falling down. Tobacco has also completely replaced the morphine use, but he did refer to his 7% cocaine solution in one episode.
It was just a treat.

Actually, if you paid attention to the episode he reveals his use of the Nicotine patches, he says its next to impossible to keep a smoking habit in London "nowadays" this is likely due to some form of legislation limiting areas where one can smoke or additional taxes on them. While Mycroft most likely extends this due to the loss of Irene Addler as well, it is also because of some form of restriction to smokers in London. At least, that is my analysis without checking in on British law.

It was a way of testing how upset Sherlock was. In the Hounds of Baskerville, Sherlock is extremely stressed out because he doesn't have a case to work on, and can be seen trashing the flat looking for a pack of cigarettes.
When someone comes with a case, Sherlock begs him to smoke (since the person smoked) and then sniffs out all the smoke.

So, since Sherlock was upset, he took the cigarette. That's why John swears when he finds out.

I saw it as a test to see how upset he was about Irene. When he took it and Mycroft spoke to John, he was worried about it being a 'danger night' and Sherlock taking the cigarette provided him with the proof that that night could potentially be one.